Question 35

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waecmaths question: 

In the diagram, PQR is a straight line, QRST  is a parallelogram$\angle TPQ={{72}^{\circ }}$ and $\angle RST={{126}^{\circ }}$. What type of triangle is ΔPQT

Option A: 

An equilateral triangle

Option B: 

A right angled triangle

Option C: 

An Isosceles triangle

Option D: 

A scalene triangle

waecmaths solution: 

$\begin{align}  & \angle TQR=\angle TSR={{126}^{\circ }}\text{   }\!\!\{\!\!\text{ opposite }\angle s\text{ of a }\text{ are equal}\} \\ & \angle TQP={{180}^{\circ }}-\angle TQR={{180}^{\circ }}-{{126}^{\circ }}={{54}^{\circ }}\text{  }\!\!\{\!\!\text{ sum of }\angle s\text{ a straight line }\!\!\}\!\!\text{ } \\ & \vartriangle TPQ \\ & \angle PTQ={{180}^{\circ }}-(\angle TQP+\angle TPQ)={{180}^{\circ }}-({{72}^{\circ }}+{{54}^{\circ }})={{54}^{\circ }} \\ & \vartriangle PQT\text{ is an isosceles triangle}\text{.} \\\end{align}$

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